SUMMARY

It is commonly assumed that the facial pit of pitvipers forms relatively
sharp images and can detect small differences in environmental surface
temperatures. We have visualized the temperature contrast images formed on the
facial pit membrane using a detailed optical and heat transfer analysis, which
includes heat transfer through the air in the pit chambers as well as
via thermal infrared radiation. We find the image on the membrane to
be poorly focused and of very low temperature contrast. Heat flow through the
air in the pit chambers severely limits sensitivity, particularly for small
animals with small facial pit chambers. The aperture of the facial pit appears
to be larger than is optimal for detecting small targets such as prey at 0.5
m. Angular resolution (i.e. sharpness) and image strength and contrast vary
complexly with the size of the pit opening. As a result, the patterns of
natural background temperatures obscure prey items and other environmental
features, creating false patterns. Consequently, snakes cannot simply target
the strongest signal to strike prey. To account for observed behavioral
capabilities, the sensory endings on the pit membrane apparently must respond
to temperature contrasts of 0.001°C or less. While neural image sharpening
likely enhances imaging performance, it appears important for foraging snakes
to select ambush sites offering uniform backgrounds and strong thermal
contrasts. As the ancestral facial pit was likely less sensitive than the
current organ, objects with strong thermal signals, such as habitat features,
were needed to drive the evolution of this remarkable sense.

Introduction

It has been known for some time that the eponymous facial pits of pitvipers
(Viperidae: Crotalinae) are sense organs that respond to thermal infrared
radiation emitted by nearby surfaces (ca. 5–30 μm wavelength), and
can thereby sense the temperature of surrounding surfaces
(Bullock and Cowles, 1952).
Functionally, the facial pits are image-forming structures based on pinhole
optics resembling the chamber-type eye of the nautilus
(Fernald, 2006). We have a
general sense of some behavioral functions, and various aspects of the anatomy
and neurophysiology of the facial pit are well documented. But, we lack clear
understanding of the physical and physiological optics of the facial pit
system, and thus of what pitvipers can actually `see' with the facial
pits.

Anatomically, the facial pits are located between the eyes and nostrils
(Fig. 1A). Each consists of a
1–3 mm diameter aperture expanding internally to form an asymmetric and
somewhat irregular mushroom-shaped cavity
(Fig. 1B). Thermal radiation
entering the aperture falls on and heats a sensory membrane suspended in the
back of the pit, dividing the pit cavity into an inner and outer chamber. The
membrane contains a few thousand receptors that respond to membrane
temperature changes of 0.003°C or less
(Bullock and Cowles, 1952;
Bullock and Diecke, 1956;
de Cock Buning, 1983;
Moiseenkova et al., 2003).

The design and interpretation of studies of both behavioral responses and
neural processing requires knowledge of the temperature contrast image on the
membrane, which is defined by the optical and the heat transfer properties of
the facial pit. Angular resolution (the sharpness of the image) determines the
`brightness' of small targets, the extent to which larger objects such as food
items contrast with background clutter, and the overall quality of spatial
information available for tasks such as general navigation and
thermoregulation. Background and target surface temperatures as well as
surface temperature contrasts are affected by air temperature, current and
past solar radiation, and the heat storage capacity of the object. Thus,
thermal contrast varies with habitat structure and time of day, creating
spatiotemporal variation in the probability of success of behavioral
activities hinging on thermal cues.

(A) Close-up view of the head of a western diamondback rattlesnake
Crotalus atrox Baird and Girard 1853 showing the location of the pit
organ. (B) Frontal section showing the internal structure of the pit organ of
a Pacific rattlesnake Crotalus o. oreganus Holbrook 1840. To aid
visualization, the anterior air chamber was filled with red acrylic before the
entire head was infiltrated and embedded. However, this may have displaced the
membrane closer to the back of the posterior chamber. The angular apertureθ
i varies from 23° (included angle 45°) laterally to
10° (included angle 20°) when looking ahead and to the contralateral
side.

Limited understanding of the relevant optical and thermal physics of the
facial pits is a common deficiency of existing studies. For example, a
theoretical analysis of pit sensitivity
(Jones et al., 2001) severely
overestimated absorption of thermal radiation by the atmosphere and concluded
that absorption limited the pit organ to a range of a few cm
(Bakken, 2007). A number of
researchers have presented pitvipers with thermal stimuli having surface
temperatures equal to or exceeding body core temperature of typical prey items
(e.g. Bullock and Barrett,
1968; Goris et al.,
2000; Goris and Nomoto,
1967; Hartline et al.,
1978; Pappas et al.,
2004). However, the furred and feathered surfaces covering most of
the body are actually closer to air temperature (e.g.
Hill et al., 1980;
Hill and Veghte, 1976;
Kardong, 1986;
Veghte and Herreid, 1965).
Behavioral experiments have typically used a single target against a uniform
thermal background. This may overestimate performance in natural habitats,
because the angular resolution of the pit organ is likely poor
(Otto, 1972;
Stanford and Hartline, 1984).
As a result, the radiation from small, warm objects is spread over a large
area of the pit membrane and blended with non-uniform natural thermal
backgrounds. The only experimental study known to have examined background
effects (Theodoratus et al.,
1997) placed test targets behind aquarium glass, which is
completely opaque to thermal radiation
(Hsieh and Su, 1979).
Consequently, the reported responses are experimental artifacts.

The foregoing review shows that there is a need for a comprehensive study
that will define the input to the sensory system of a pitviper under relevant
natural situations. Such a study requires detailed knowledge of the physical
optics of the facial pit and its heat transfer properties. Prior studies
(de Cock Buning, 1984;
Otto, 1972) examined the
distribution of radiation from a point source over the pit membrane using
simplified geometric models, but lacked the modern computational tools needed
to translate this information into a representation of the temperature
contrast image on the pit membrane. Further, these studies omitted potentially
important heat transfer processes such as convection and conduction from the
pit membrane.

To fill this need, we have analyzed the facial pit as an optical system and
used heat transfer analysis to convert image irradiance to membrane
temperatures on the basis of published physiological data. We then obtained
radiometric thermograms of some realistic natural habitats to determine the
typical surface temperatures and temperature contrasts present. Finally, we
used the results of our optical and heat transfer analysis and image
processing software to manipulate these thermograms to generate corresponding
representations of the image falling on the facial pit membrane. The processed
images indicate the general characteristics of the sensory input to the facial
pit sensory system in various ecologically meaningful situations, and provide
insights that can aid the design and interpretation of behavioral and
neurophysiological studies.

Theory: optics of the pit organ

Overview

The facial pit is essentially a pinhole camera consisting of a lensless
aperture in front of a detector (the pit membrane) that forms the image plane
(Fig. 1B). Radiation simply
passes through an opening (the optical pupil) without deflection and falls on
the image plane. Facial pit apertures are large enough relative to pit depth
that diffraction may be neglected, and thus elementary geometric optics and
photometric analysis can be used (Born and
Wolf, 1970). Briefly, the light from a point on the source object
that passes through the aperture irradiates a defined area on the image plane,
called the point spread function. The image is formed by overlapping spread
functions, and, as demonstrated later, is either sharp but dim when the
optical pupil is small, or bright but blurred when it is large. We will follow
de Cock Buning (de Cock Buning,
1984) and model the facial pit as a circular aperture of radius
ra located a distance d from the image plane
(Fig. 2). Though a
simplification of the geometry in Fig.
1B, this model is adequate to illustrate the main features of the
optics of the facial pit. The analysis proceeds in three steps and follows
standard procedures (Born and Wolf,
1970).

Radiometry of the ideal image

The first step is to define the ideal (perfectly focused) image. This is
found by tracing the chief ray, i.e. the line passing from a point on the
source object through the center of the pinhole aperture to the corresponding
point on the image plane. All of the radiant energy from a point on the source
that passes through the aperture is assumed to fall on the corresponding point
of the image (Born and Wolf,
1970).

Both source and image are characterized by their radiance B (W
m–2 sr), defined as the radiant flux, dΦ (W) per unit
solid angle ω (steradians) emitted by or falling on an element of
surface area dA (m2). Source and image radiance can be
related to the surface temperature of the source object,
To (kelvins, K=273.15+°C; absolute temperatures in
kelvins must be used in thermal radiation calculations; temperature
differences or changes may be either K or °C). The total radiant fluxΦ
(W) emitted from dA is given by the Stefan–Boltzmann law,
(1)
where σ=5.67×10–8 W m–2
K–4, and the emittance of the surface is ϵ
(0⩽ϵ⩽1). Total radiant flux may also be computed by integrating
source radiance Bo over a hemispherical solid angle,
(2)
where θ and ϕ are spherical coordinates. Combining
Eqn 1 and
Eqn 2 gives the relation between
radiance and object temperature:
(3)
There are no optical elements, and thus no reflection or absorption losses in
pinhole optics. Thus, conservation of energy requires that the radiance of the
image Bi equals the radiance of the source object
Bo (Born and Wolf,
1970).

Spherical coordinate system used in Eqn
2 and Eqn 4 to
compute radiance and irradiance. The symbol dω=sinθdθdϕ
denotes an element of solid angle.

The temperature at a point on the membrane is determined by the local
balance between radiant heat transferred from the source object and other
sources of heat gain and loss. The heat storage capacity of the membrane is
important only for transient stimuli. Lateral conduction within the membrane
may reduce angular resolution somewhat
(DeSalvo and Hartline, 1978),
but has a negligible effect on the heat balance.

The total irradiance (W m–2) at an image point
(x,y) on the pit membrane is the sum of the image irradiance from the
source object Ei(x,y), plus the background
irradiance from the various walls of the pit, Qpit. The
image irradiance is found by integrating the image radiance
Bi=Bo over the solid angle of the exit
pupil, i.e. over the pinhole aperture as seen from (x,y). For our
facial pit model, a simple circular aperture of radius ra
a distance d from the image plane
(Fig. 2), the exit pupil is a
circle with its center normal to point (x,y), subtending a half-angle
of θi=arctan (ra/d). Integrating
over the solid angle subtended by this exit pupil and applying
Eqn 3, the image irradiance is:
(4)
Heat is exchanged between the facial pit membrane and the surrounding air
primarily by conduction. The membrane is shielded from forced convection by
its location in a semi-enclosed pit
(Bullock and Diecke, 1956),
and wind speed near the ground is very low
(Gates, 1980). For free
convection to occur within an enclosure, the Grashof number Gr must exceed
1000 (Eckert and Carlson,
1961). As Gr1000
for a facial pit with dimensions of 2–5 mm and a temperature difference
between membrane and pit wall of a few °C, free convection is absent.

Conductive heat transfer through the air inside the pit chambers from a
point on the membrane at a temperature T to the opposite pit wall at
a temperature Tp is approximately
(5)
Here, Qair is the amount of heat lost by conduction
through the air to the pit walls (W m–2), k is the
thermal conductivity of air (0.026 W m–1 °C or W
m–1 K), z is the effective distance from the
membrane to the wall of the outer (anterior) chamber, and w is the
effective distance to the wall of the inner (posterior) chamber.

At any point on the pit membrane (x,y), the energy lost by
radiation and convection from both sides of the membrane must equal the
radiant energy gained from the pit walls, Qpit, and from
the source object, Ei. If the temperature of an image
point denoted by subscript 1 is and the
temperature of the corresponding source object point is
T1, then:
(6a)
Substituting for E1 using
Eqn 4,
(6b)
If the temperature of an image point denoted by subscript 2 is
and the temperature of the
corresponding object point is T2, then:
(7)
The factor of 2 on the left side of Eqn 6 and
Eqn 7accounts for the emission of
thermal radiation from both the front and back surfaces of the pit
membrane.

The facial pit membrane responds to the contrast between a target and its
background,
(),
rather than absolute temperature (Bullock
and Barrett, 1968; Grace and
Van Dyke, 2005). The temperature contrast of the ideal image is
given by combining Eqn 6 and Eqn
7,
(8)
By Kirchoff's law (conservation of energy), the membrane emittance for thermal
radiation ϵm equals its absorptance, αm, and
thus for simplicity we use only ϵm. As natural surfaces haveϵ≅
0.95–0.97, Eqn
8 has been further simplified by the approximationϵ
=1.

Under natural conditions, the differences among snake, object, and
background temperatures are small (ca. ⩽10 K) compared to their absolute
temperatures (ca. 300 K). This allows Eqn
8 to be linearized about a convenient reference temperature
(Bakken, 1976), so that
.
Defining
,
the temperature contrast between points 1 and 2 is:
(9)

Computing actual image using point spread function

A pinhole camera produces a geometrically perfect image, but the radiation
from a single source point is spread over an area of the image called the
point spread function. The radiance at a given point (x,y) on the
membrane is the sum of the radiation from all the point spread functions that
overlap (x,y). Consequently, the image on the membrane is `fuzzy' and
has less contrast than the corresponding ideal image.

Mathematically, the real temperature distribution over the image plane
T′(x,y), is found by convoluting the temperature
distribution of the ideal image,
, with the point
spread function S(x–ξ,
y–ζ). Here, (x,y) is the coordinate of
the point of interest and (ξ,ζ) is the coordinate of an ideal image
point contributing energy to (x,y). Strictly, the convolution should
precede the heat transfer calculation, but this procedure is computationally
more convenient and the final result is the same because the relation between
irradiance and temperature (Eqn
9) is effectively linear.

For our model of the facial pit (Fig.
2), the point spread function is approximately
(10)
The real temperature contrast image is computed using
(11)
Conservation of energy requires that the result be normalized by the integral
of the spread function (denominator).

Materials and methods

To investigate the consequences of variation in the spatial resolution and
receptor sensitivity of real and hypothetical facial pits, we derived
representations of the blurred image on the pit membrane using the above
analysis. As approximations to the ideal image, we used sharply focused
thermograms of various scenes recorded with a resolution of 0.1°C and an
absolute accuracy of 1–2°C using a FLIR PM575 radiometric thermal
imager (FLIR Inc, North Billerica, MA, USA). We computed the membrane
temperature contrasts using Eqn
9, and then convoluted these images using
Eqn 11 as implemented in MATLAB
(The MathWorks, Inc. Natick, MA, USA). We used the `circular' option in MATLAB
to reduce edge artifacts. The output is our representation of the approximate
appearance of the temperature contrast images on the pit membrane.

We explored the interrelated effects of angular aperture on image sharpness
and membrane temperature contrast by using spread functions withθ
i from 2.5° to 20°. The observed angular apertures
for Crotalus oreganus (Fig.
1B) are ca θi=20–30° to the side, and
ca. 10° in the forward direction (see also
DeSalvo and Hartline, 1978).
The importance of forward imaging is indicated by a higher density of
receptors and associated blood vessels on the portion of the membrane
corresponding to objects directly in front of the head
(Amemiya et al., 1999;
Goris and Nomoto, 1967;
Goris and Terishima, 1973).
Viewed from the forward direction, the external aperture is higher than it is
wide (Fig. 1A) and the optical
spread function is therefore sub-elliptical. To simulate this, we used
elliptical spread functions with the horizontal θi half of
the vertical θi.

(A) Thermogram of an Ord's kangaroo rat Dipodomys ordii taken in a
laboratory enclosure set at 15°C, scaled to represent an 80° field of
view with the animal 25 cm distant. (B–D) The results of convoluting
that image with circular spread functions with the indicated half-anglesθ
i). (E) The same animal imaged at 30°C. Both A and E use
the same color representation of temperature and are marked with the full
range of temperatures visible in each. (F–H) The results of convoluting
that image. The color steps in B–D and F–H indicate temperature
contrasts of 0.001°C. While spatial resolution is good at 15°C for the
hypothetical θi=5°(D), contrast is only 0.003°C and
the kangaroo rat is essentially invisible at 30°C (H). Temperature
contrast is somewhat greater for θi=10° and 20°,
0.006°C in the 15°C cabinet, and 0.002–0.003°C in the
30°C cabinet.

Bullock and Diecke (Bullock and Diecke,
1956) estimated the sensitivity of the pit membrane to temperature
differences as <0.001°C to 0.003°C because they obtained a response
to even the smallest temperature difference they could measure, 0.0025°C.
They also found that neural response is roughly linear for temperature
contrast up to 100× threshold sensitivity. To relate images to this
membrane sensitivity, we set the temperature range and the number of colorbar
steps such that each of the 30 colorbar steps would represent a membrane
temperature difference equivalent to presumed temperature sensitivities within
this range.

Results

Signal strength and ambient temperature

Environmental conditions have a strong effect on source temperature
contrasts, particularly for mammalian and avian prey. The surface temperature
of fur or feather insulation is closer to air than body core temperature (e.g.
Hill et al., 1980;
Hill and Veghte, 1976;
Kardong, 1986;
Veghte and Herreid, 1965). To
illustrate, we recorded thermograms (Fig.
3A,E) of a potential prey item in a temperature cabinet at the
lowest body temperature of active rattlesnakes, 15°C, and at the typical
hunting temperature of 30°C (Beck,
1995; Hirth and King,
1969; Moore,
1978). While the temperature contrast over most of the 60 g Ord's
kangaroo rat Dipodomys ordii is greatest at 15°C, over most of
the fur surface it is only about 6°C above air temperature. This is less
than 1/3 of the 21°C difference between body core (36°C) and air
temperature. At 30°C, temperature contrast is about 2.5°C, compared to
the 6°C difference between core and air. Only the eyes have a surface
temperature near body core temperature. The results for other bird and mammal
prey items we examined are similar, although some thinly furred ground
squirrels had higher fur temperatures.

Angular aperture, resolution, and signal strength

The size of the angular aperture of the pit influences both resolution and
signal strength. Fig.
3B–D,F–H are representations of the temperature
contrast images on the membrane of a 3 mm total diameter pit with the membrane
located 0.75 mm from the back wall and various θi from
20° to 5°. Colorbar steps correspond to membrane temperature
differences of 0.001°C, near the lower end of the sensitivity range
suggested by Bullock and Diecke (Bullock
and Diecke, 1956). Resolution is lower but temperature contrast is
greater for larger pit apertures.

Non-uniform background effects

The laboratory images have a uniform contrasting background, while natural
thermal backgrounds are strongly patterned. To investigate the potential
impact of background pattern on prey targeting, we recorded outdoor thermal
images of a variety of targets. Fig.
4A is an image of two mice recorded in open scrub habitat at
midnight following a mostly cloudy day. Based on
Fig. 3, thermal imaging
conditions were nearly optimal for the snake (air temperature, 15°C;
surface temperature 11–13°C). Nevertheless, the contrast of the
convoluted images (Fig.
4B–H) is low and the mice hard to detect with color steps of
0.001°C. For clarity, we exaggerated contrast by using color steps of
0.0005°C.

Fig. 4B–D are
visualizations of the case where mice are viewed along the pit axis by
convoluting the thermogram with various circular spread functions withθ
i from 5° to 20°, while
Fig. 4E–G visualize mice
directly in front of the snake by using elliptical spread functions ofθ
i from 5°×2.5° to 20°×10°
(vertical × horizontal). These values are based on anatomy of the facial
pit (Fig. 1B). Forθ
i=10° and 20°, the angular dimensions of the mice
are much less than θi, and their thermal radiation is smeared
over a large area of the pit membrane. Consequently, the mice are indicated
not by the highest temperature, but by an overall circular or elliptical
pattern superimposed on the background. The highest membrane temperatures are
created by a large background area that is only slightly warmer than average.
Consequently, in an outdoor environment, a pitviper cannot simply target the
strongest signal.

(A) Thermogram of two mice, scaled for an 80° field of view with the
animals 45 cm distant. Images were recorded at an air temperature of 15°C
in sparse scrub habitat around midnight, following a mostly cloudy afternoon.
(B–D) Image A convoluted with circular spread functions chosen to
visualize the image along the optic axis of the facial pit. (E–G) Image
A convoluted with elliptical spread functions to visualize imaging directly in
front of the snake (right column). The θi indicated for each
row is the aperture angle of a circular spread function (B–D), and the
vertical θi of an elliptical spread function (E–G). The
minor axis θi of the ellipse is half that of the vertical
axis. The temperature contrast in these images is quite low, so for clarity we
have assumed a larger pit and greater membrane sensitivity (color steps of
0.0005°C) than in Fig. 3.
Note that, particularly for large θi (poor resolution), the
warmest part of the image is a large, warm area of ground and not the
mice.

Effect of conduction through still air in the pit on the ratio of image to
source temperature contrast for facial pits with θi=20°
and various dimensions and membrane positions. The x-axis is the
thickness of the posterior chamber and indicates the position of the membrane
from touching the back of the posterior chamber (thickness 0) to the center of
the chamber (thickness equal to half the total thickness of the pit), as
indicated by the inset drawings based on
Fig. 1B. The y-axis is
the temperature contrast on the pit membrane for a 1°C source temperature
contrast. If conduction through the air surrounding the membrane is neglected
as in prior studies, this ratio is 0.058 for pits of all sizes and
configurations.

Sensitivity and conduction through air in the pit cavities

The low membrane temperature contrasts evident in Figs
3 and
4 are largely the result of
signal loss by heat conduction through air to the walls of the facial pit
cavity. The dimensions of the posterior chamber are particularly important, as
the membrane generally lies near the back wall of the facial pit and the
smallest dimension dominates heat loss (Eqn
5). A given scene will produce less temperature contrast on the
membrane of snakes with smaller facial pits or when the membrane lies nearer
the pit wall (Fig. 5) because
conduction is inversely proportional to distance.

The consequences of varying facial pit dimensions are visualized in
Fig. 6. We computed temperature
contrast images for facial pits from 1 to 4 mm total thickness with the pit
membrane 25% of the total thickness from the wall of the posterior chamber and
both circular (Fig. 6B–D)
and elliptical (Fig.
6E–G) spread functions with θi=20°.
Even assuming a high membrane sensitivity (color steps 0.0005°C), the mice
are indistinct to invisible when the total thickness of the facial pit is 2 mm
thick or less.

Scenes presenting strong thermal contrast

We have previously suggested (Krochmal
and Bakken, 2003) that thermoregulation represented the initial
adaptive force that drove the evolution of the facial pits because the
ancestral pit was likely insensitive, and environmental features are larger
than prey items and typically show greater temperature contrast in daylight
and early evening. This is illustrated in
Fig. 7A–D, which show a
desert rodent burrow that might provide the snake with a refuge from the heat.
The burrow is clearly visible even with the smallest
(θi=5°) aperture (membrane temperature contrast
0.008°C), and is least evident for θi=20° due to
background interference.

The effect of facial pit size on membrane temperature contrast. The
original thermogram (A) used in Fig.
4 has been processed to show membrane temperature contrasts for
facial pits both on the optic axis of the pit (B–D) and directly in
front of the snake (E–G). The total thickness, including both the outer
and inner chambers, is indicated for each row. The membrane is assumed to be
25% of the total diameter from the wall of the posterior chamber. The
temperature contrast on the pit membrane is indicated by color steps of
0.0005°C.

Another situation providing strong contrast against background is a
warm-blooded prey item viewed against a clear sky, which emits little thermal
radiation (Swinbank, 1963).
This is illustrated in Fig.
7E–H, which shows a cardinal (Cardinalis
cardinalis) viewed against the sky at an air temperature of 20°C. The
5°C radiant temperature of the sky contrasts strongly with the 30°C
feather surface temperature of the bird, and creates an 0.01°C membrane
temperature contrast even with the smallest angular aperture
(θi=5°).

Discussion

Signal loss by conduction through air and estimates of receptor
sensitivity

Our findings indicate either that the membrane is more sensitive than
currently estimated, or that pitvipers obtain less information from this sense
than is commonly believed. Accounting for conductive heat loss through still
air in the anterior and posterior chambers reduces the temperature contrast of
the image to only 5–25% of that estimated by earlier studies, which did
not consider conduction through the air
(Fig. 5). To achieve the
observed behavioral capabilities of pitvipers
(Ebert and Westhoff, 2006),
the contrast sensitivity of the pit membrane needs to be at the most sensitive
end of the range (0.003–0.001°C) found by Bullock and Diecke
(Bullock and Diecke, 1956).
Our analysis assumed the snake was on the ground, and thus did not include
forced convection. Significant air movement with the exterior pit, e.g.
because the snake was exposed to wind on an arboreal perch, would further
reduce membrane temperature contrasts. Thus, the membrane may conceivably
respond to contrasts of less than 0.001°C. The mechanism by which such
sensitivity might be obtained is presently unknown.

Movement and time response

To simplify this preliminary study, we chose not to examine the effects of
either heat storage in the pit membrane or target movement. Heat storage in
the pit membrane would potentially slow the time response and cause blurring
of moving targets. Experimental studies have reported maximum flicker fusion
frequencies of 8 Hz or less, depending on flicker contrast
(Bullock and Diecke, 1956).
Goris et al. (Goris et al.,
2000) has suggested that neurological control of pit membrane
microcirculation may serve to increase time response, but this has not been
demonstrated experimentally. Membrane receptor response is commonly regarded
as phasic (Barrett et al.,
1970; Bullock and Cowles,
1952) although some studies have reported tonic and phasic-tonic
responses as well (Goris and Terishima,
1973). A primarily phasic response would presumably make the
facial pit more sensitive to moving targets than stationary ones, although
scanning head movements could make stationary targets equally conspicuous
(Goris and Terishima, 1973).
Behavioral and modeling studies are needed to confirm that these conclusions
apply to overall sensory performance.

Growth and facial pit sensitivity

The effect of conductive heat loss through the air is inversely
proportional to pit size. This suggests that the facial pit may be of limited
value to juvenile snakes. Possibly as a result, juvenile pitvipers are known
to depend more on ectothermic prey than do adults, although body size is also
a factor. The observations that juvenile Gloydius shedaoensis
preferentially select arboreal ambush sites where prey are viewed against the
cool sky (Fig. 7E–H), and
are slower and less accurate in their strikes
(Shine et al., 2002b) might be
explained by the reduced sensitivity of their smaller facial pit organs.
However, direct evidence with which to test this hypothesis is lacking.

Two situations relevant to pitviper biology present particularly strong
surface temperature contrasts. (A) A rodent burrow below a desert shrub at
high noon, scaled to an 80° view angle with the burrow 28 cm distant.
Conditions are warm but not extreme, with air temperature of 33°C and peak
ground temperatures near 50°C. (B–D) Pit membrane temperature
contrasts visualized using the indicated θi. The burrow could
be easily identified from a distance by a snake leaving the shade of a bush to
seek underground shelter. (E) An American cardinal Cardinalis
cardinalis viewed against a clear sky, scaled to an 80° view angle
with the cardinal 31 cm distant. Note that the thermal imager does not record
radiant sky temperature properly, and so the sky has been rescaled to a
radiant temperature of 5°C on the basis of Swinbank's formula
(Swinbank, 1963). (F–H)
Pit membrane temperature contrasts visualized using the θi
indicated for that row. The temperature contrast on the pit membrane in
B–D and F–H are indicated by color steps of 0.001°C.

Is the angular aperture of the facial pit optimal?

Once the full angle of the facial pit (2θi) exceeds the
angle subtended by the target, membrane irradiance is constant and the only
effect of further enlarging the aperture is to impair resolution and increase
background interference. In Fig.
3, the kangaroo rat at 0.5 m subtends a full angle of 10°, so
that the optimal half angle θi is 5°, much smaller than
the actual 10–22° θi of C. oreganus
(Fig. 1B). As is evident in
Figs 4 and
7, a small aperture may be
advantageous even when target irradiance on the pit membrane is somewhat
reduced because background interference is decreased more than the contrast
between target and background. Thus, the facial pit aperture appears to be
larger than optimal for detecting small objects, like prey, and it is not
clear why the angular aperture of the facial pit is as large
(θi=20–30°) as is observed. A large aperture
provides more detectable contrast and might be used to reconstruct images with
more angular resolution and contrast than could be produced with a smaller
aperture. Similarly, the aperture might be optimized for detecting larger
objects, including environmental features. This could facilitate behavioral
thermoregulation, which has been proposed as the initial adaptive force that
drove the evolution of the organ (Krochmal
and Bakken, 2003).

Utilizing low angular resolution imaging

Several simple mechanisms have been proposed to explain how pits may
function despite apparently low spatial resolution, including edge detection
or the use of both pits as a null detector (e.g.
Goris and Terishima, 1973).
Our results call into question the utility of such simple mechanisms.
Specifically, the spread function resulting from a large aperture blurs the
edges of real targets, and the warmest part of the pit membrane may not
represent the target when the background is not uniform
(Fig. 4B,E).

A more credible alternative is that the imaging properties of the facial
pit may be improved by image sharpening during post-processing in the central
nervous system. If the blurred image has sufficiently fine discrimination of
irradiance levels, and if the optical spread function is known, the inverse
operation of Eqn 11 can
reconstruct the original image in some detail. Image sharpening routines are
included in many image processing programs such as MATLAB, and a hypothetical
neural network procedure has been proposed specifically for pitvipers
(Sichert et al., 2006), though
empirical data to support it is lacking.

The quality of the processed image is closely linked to how accurately the
spread function is known [chapter 5, Gonzalez and Wintz
(Gonzalez and Wintz, 1977)].
The geometry of the facial pit, and thus the spread function, varies only with
growth, if at all. Thus, the snake's neural network can potentially learn a
single spread function, which can then be used to sharpen images. Indeed, it
has been reported that the temperature contrast image on the facial pit
membrane is sharpened by neural processing in the lateral descending
trigeminal tract (LTTD) of the medulla
(Berson and Hartline, 1988;
Stanford and Hartline,
1980).

The spread function might be provided in two ways. First, neural
interconnections between thermal and visual neurons have been reported in the
optic tectum (Berson and Hartline,
1988; Hartline et al.,
1978). It has been shown that some alternative spatial senses,
such as acoustic prey location in owls, are fine-tuned to match visual input
(Harris, 1986;
Schnitzler et al., 2003), and
the same may be true for the facial pit. Second, spread functions might be
determined from facial pit input by using neural mechanisms analogous to
forensic computer algorithms [chapter 5, Gonzalez and Wintz
(Gonzalez and Wintz, 1977)] or
the autofocus mechanism found in some cameras.

Foraging strategies and thermal backgrounds

Pitvipers commonly use an ambush foraging strategy (e.g.
Reinert et al., 1984), and the
coupled problems of thermal signal strength and angular resolution that we
have documented suggest that predation effectiveness would be greater if
pitvipers were to seek out ambush sites offering a contrasting and relatively
uniform thermal background. Shine and Sun
(Shine and Sun, 2002)
conducted a 2-day study of thermal and visual background in pitvipers foraging
on migrating birds and found that snakes indeed selected ambush sites that
offered a cool sky background. Although snakes struck preferentially at warm
targets, the importance of the facial pits was not entirely clear. The snakes
generally left arboreal perches during the night and returned in the morning,
and thus foraged primarily when ample visual illumination was available.
Further, site selection was equally consistent with selecting areas of highest
prey availability. Thermoregulation is another factor that might influence
ambush site selection (Shine et al.,
2002a). Clearly, this is a complex problem needing carefully
designed field studies.

Facial pit evolution and scenes presenting strong thermal
contrast

The ancestral facial pit likely had lower angular resolution and less
temperature sensitivity than the modern organ. Thus, evolution of the facial
pit is most likely to have occurred in a situation where large targets with
strong temperature contrast were present, and the ability to sense them
provided a selective advantage (Krochmal
and Bakken, 2003; Krochmal et
al., 2004). At least two situations provide high contrast
(Fig. 7). First, the ability to
sense thermal radiation may allow a snake to thermoregulate more effectively
in a habitat characterized by strong temperature contrasts caused by solar
radiation (Krochmal and Bakken,
2003). This scenario also provides large targets, minimizing the
demands on angular resolution. Second, perching birds contrast strongly
against the sky (Shine and Sun,
2002). Thus, although most extant pitvipers are heavy bodied and
terrestrial in habit, the facial pits may have evolved initially to facilitate
nocturnal predation on roosting birds or active bats in sparse deciduous
vegetation, where they would be viewed against a clear night sky. The radiant
temperature of a night sky is well below air temperature
(Swinbank, 1963), so birds and
mammals would contrast even if the insulating coat is at air temperature. A
similar, but less extreme, contrast may exist between burrowing mammals and
the burrow walls. Although most pitvipers are sedentary, many other snakes
actively search burrows (Secor,
1995), and so the facial pit may have evolved initially to aid in
burrow searching. To test these hypotheses, studies are needed to determine
how extensively extant pitvipers use the facial pit sense in habitats imposing
different thermal radiation backgrounds and different thermoregulatory
demands. Careful attention to paleohabitat signatures associated with any
discoveries of fossils of putative ancestral pitvipers might also indicate the
relative merit of these scenarios.

Summation

Our survey of the approximate imaging properties of the facial pits leads
us to conclude that the imaging properties of the pit organ are critical to
understanding its function as a sensory organ and its role in the behavior and
ecology of the animal. While there has been significant progress, many
interesting studies of field and laboratory behavior and sensory
neurophysiology remain to be done before we will fully understand this novel
sensory organ and its role in the ecology of pitvipers.

List of symbols

Φ

radiant flux (W)

ω

solid angle (sr; steradians)

ϵ

emittance for thermal infrared radiation (0⩽ϵ⩽1)
(dimensionless)

θ

spherical coordinate (rad)

θi

half-angle of facial pit aperture as seen from (x,y) on pit
membrane, θi=arctan (ra/d)
(rad)

ϕ

spherical coordinate (rad)

(ξ,ζ)

coordinate of ideal image point contributing energy to
(x,y)

(x,y)

coordinates of an image point of interest (m)

A

area (m2)

d

distance from aperture center to image plane (m)

dω

element of solid angle (sr)

dA

element of surface area (m2)

Ei(x,y)

irradiance at image point (x,y) due to source object (W
m–2)

Gr

Grashof number (dimensionless)

Qair

heat flow through the air to the pit wall by conduction (W
m–2)

Qpit

background irradiance from pit walls falling on an image point (W
m–2)

R

equivalent conductance due to thermal radiation,
R=4σϵmTp3 (W
m–2 °C)

ra

facial pit aperture radius (m)

S(x–ξ, y–ζ)

point spread function

T

membrane temperature at any particular point (°C or K)

temperature of the ideal image at point (ξ,ζ)

T1`

temperature of the source object point corresponding to
T1 (°C or K)

To

surface temperature of the source object (K)

Tp

pit wall temperature (°C or K)

w

effective distance from membrane to the wall of the inner (posterior)
chamber (m)

z

effective distance from membrane to the wall of the outer (anterior)
chamber (m)

k

thermal conductivity of air, k=0.026

T1

temperature at point 1 on pit membrane (°C or K)

B

radiance (W m–2 sr)

Bi

radiance of the image (W m–2 sr)

Bo

source (W m–2 sr)

E

irradiance (W m–2)

σ

Stefan-Boltzmann constant, 5.67×10–8 (W
m–2 K–4)

ACKNOWLEDGEMENTS

We thank Marilyn Banta for the use of her laboratory to take thermal images
of the kangaroo rat in her teaching collection, University of Northern
Colorado IACAUC protocol 0305 and Colorado Division of Wildlife Scientific
Collecting License 04-TR1014. Other thermal images were of semi-tame animals
foraging on spilled food in public campgrounds. Snake anatomy studies
(Fig. 1) were done by S.
Colayori under Indiana State University IACAUC protocol 2-10-2006:GSB/SEC, and
were supported in part by a grant from the Indiana Academy of Sciences. NSF
Grant 99-70209 provided the thermal imager, and Indiana State University
provided general support.

Similar articles

Other journals from The Company of Biologists

Neuropeptide evolution and function

Neuropeptides are a diverse assemblage of signalling molecules that have key roles in the regulation of behaviour. Understanding the evolutionary relationships and functions of the plethora of neuropeptides has presented a considerable challenge to biologists. Based on presentations and discussions at a Royal Society meeting in 2017, three companion Review articles by Elphick et al., Jékely et al. and DeLaney et al. discuss advances in our knowledge of neuropeptide evolution and function and the techniques that have facilitated progress in this field of research.

The exquisite bright colours of Pachyrhynchus weevils were thought by Alfred Russel Wallace to warn off potential predators, but whether this warning related to their hard exteriors, their spiky legs or some irritating taste had never been tested. Now, a century and half later, a team from Taiwan revisits this question and suggest that hardness itself acts as an effective secondary defence.

In our latest early-career researcher interview, Brooke Flammang, Assistant Professor at the New Jersey Institute of Technology, tells us about her research journey (including writing her Master's thesis in an ambulance while working as a paramedic), the importance of collaboration in integrative biology, and her approach to teaching.

"The paper provided the first quantitative field evidence of the way that animals might gain protection from predation by seeking cover in a group of other similar animals. This protection is known as the dilution effect."

William Foster discusses ‘Evidence for the dilution effect in the selfish herd from fish predation on a marine insect’, the 1981 classic he published in Nature with John Treherne, former JEB Editor-in-Chief.